The present invention relates to a new and distinct variety of flat nectarine tree, Prunus persica var. nucipersica, which has been given the variety denomination ‘ASFNBF0688’. This new tree produces fruit with a long shelf life without alteration both on the tree after growth completion and after harvesting, very good eating quality, semi-clingstone white flesh fruit for fresh market in the end of August to beginning of September in the Pyrénées-Orientales departement, France. Contrast is made to ‘Maillarflat’ (Sweetcap) (non-patented) white flat peach tree, ‘Redpearl’ (non-patented) yellow nectarine tree and ‘Flataugust’ (non-patented) white flat peach tree, standard varieties, for reliable description. ‘ASFNBF0688’ is a promising candidate for commercial success in that it has very attractive fruits with very long shelf life without alteration before after harvesting.